New fat Higgs: Increasing the MSSM Higgs mass with natural gauge unification

In this paper we increase the minimal supersymmetric standard model tree level Higgs mass bound to a value that is naturally larger than the LEP-II search constraint by adding to the superpotential a $\lambda S{H}_u{H}_d$ term, as in the next to minimal supersymmetric standard model, and UV completing with new strong dynamics before $\lambda$ becomes nonperturbative. Unlike other models of this type, the Higgs fields remain elementary, alleviating the supersymmetric fine-tuning problem while maintaining unification in a natural way.